Foundations Of Cognitive Science

Perceptron Paradox

Proofs of the equivalence between the mathematics of Rescorla-Wagner learning and the mathematics of perceptron learning have a long history (Gluck & Bower, 1988; Sutton & Barto, 1981).  One would imagine that the existence of proofs of the computational equivalence between Rescorla-Wagner learning and perceptron learning would mean that perceptrons would not be able to provide any new insights into classical conditioning.  However, this is not correct.  Dawson (2008) has shown that if one puts aside the formal comparison of the two types of learning, and uses perceptrons to simulate a wide variety of different classical conditioning paradigms, then some puzzling results occur.  One the one hand, perceptrons produce the same results as the Rescorla-Wagner model for many different paradigms.  Given the formal equivalence between the two types of learning, this is not surprising.  On the other hand, for some paradigms, perceptrons generate different results than those predicted from the Rescorla-Wagner model (Dawson, 2008, Chapter 7).  If the two types of learning are formally equivalent, then how is it possible for such differences to occur?  This is what Dawson (2008) called the perceptron paradox.

Dawson (2008) used the perceptron paradox to motivate a more detailed comparison between Rescorla-Wagner and perceptron learning.  He found that while these two models of learning were equivalent at the computational level of investigation, there were crucial differences between them at the algorithmic level.  In order to train a perceptron, the network must first behave (respond to an input pattern) in order for error to be computed to determine weight changes.  In contrast, Dawson showed that the Rescorla-Wagner model defines learning in such a way that behavior is not required!


  1. Dawson, M. R. W. (2008). Connectionism and classical conditioning. Comparative Cognition and Behavior Reviews, 3 (Monograph), 1-115.
  2. Gluck, M. A., & Bower, G. H. (1988). From conditioning to category learning - an adaptive network model. Journal of Experimental Psychology-General, 117(3), 227-247.
  3. Sutton, R. S., & Barto, A. G. (1981). Toward a modern theory of adaptive networks: Expectation and prediction. Psychological Review, 88(2), 135-170.

(Added April 2011)